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- Volume 55, Issue 6, 2007
Geophysical Prospecting - Volume 55, Issue 6, 2007
Volume 55, Issue 6, 2007
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Multicomponent velocity analysis with quaternions
Authors A. Grandi, A. Mazzotti and E. StucchiABSTRACTMulticomponent seismic data are acquired by orthogonal geophones that record a vectorial wavefield. Since the single component recordings are not independent, the processing should be performed jointly for all the components. A way to achieve this goal is to exploit quaternions, hyper‐complex numbers that due to their very nature are apt to represent multidimensional data. In fact, quaternion algebra allows us to extend coherence functionals used for scalar observations to multicomponent data. Therefore by means of quaternions we implement semblance and other methods based on matched filtering and on the data covariance properties.
As an application we show the results from a quaternion velocity analysis carried out combining information from the geophones and from the hydrophones of an ocean bottom cable (OBC) survey, and thus recognizing the true vectorial nature of the incoming wavefield. This also allows one to relax, at least partially, vector fidelity constraints.
We demonstrate that quaternion velocity analysis yields an improved resolution with respect to the single component velocity analysis for any coherence functional chosen and that it simultaneously evidences velocity trends pertaining to different wave modes. This facilitates the interpreter in the estimation of interval Vp/Vs by means of event correlation, and in making use of a priori information from VSP and well logs. It also speeds up the velocity picking that can be performed in a single pass on a multicomponent velocity panel, rather than once for each single component velocity panel.
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Near‐surface models in Saudi Arabia
Authors Ralph Bridle, Robert Ley and Ameerah Al‐MustafaABSTRACTA single‐layer model of the near surface throughout the Kingdom of Saudi Arabia is available. While this simple model suffices for most areas and large subsurface structures, it fails in situations where the surface topography is complex, the base of weathering is below the datum, or where the time structural closure is less than the uncertainty in the static correction. In such cases, multiple‐layered models that incorporate velocities derived from analysis of first arrivals picked from seismic shot records have proved to be successful in defining the lateral heterogeneity of the near surface. The additional velocity information obtained from this first‐arrival analysis (direct as well as refracted arrivals) vastly improves the velocity–depth model of the near surface, regardless of the topography. Static corrections computed from these detailed near‐surface velocity models have significantly enhanced subsurface image focusing, thereby reducing the uncertainty in the closure of target structures. Other non‐seismic methods have been used either to confirm qualitatively or to enhance the layer models previously mentioned. Gravity data may be particularly useful in sandy areas to confirm general structure, while geostatistical modelling of vibrator base‐plate attributes has yielded information that enhances the velocity field. In the global context, exploration targets of the oil and gas industry are seeking smaller and lower relief‐time structures. Thus, near‐surface models will need to enhance and integrate these methods, particularly in areas where the assumption of flat‐lying near‐surface layers cannot be met.
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Determining the dilation factor in 4D monitoring of compacting reservoirs by rock‐physics models
Authors José M. Carcione, Martin Landrø, Anthony F. Gangi and Fabio CavalliniABSTRACTHydrocarbon depletion and fluid injection cause compaction and stretching of the reservoir and overburden layers. 4D prestack seismic data can be used to detect these changes because compaction/stretching causes changes in traveltimes and seismic velocities. We show that, by using two different petro‐elastic models at varying effective pressures, a good approximation is to assume that the fractional changes in layer thickness, ΔL/L, and seismic velocity, Δv/v, are related by a linear function of ΔL/L. The slope of this function (the dilation factor, α= (Δv/v)/(ΔL/L)) is negative and its absolute value generally decreases (shale, low porosity) or increases (sandstone, high porosity) with increasing layer thickness and decreasing effective pressure. The analysis is mainly performed for isotropic deformations. The dilation factor for uniaxial deformations is smaller in absolute value.
The dilation factor, which can be calculated from time‐lapse data, can be used to predict reservoir compaction/stretching as a function of depth and surface subsidence.
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Stochastic inversion of pressure and saturation changes from time‐lapse multi component data
Authors Helene Hafslund Veire, Hilde Grude Borgos and Martin LandrøABSTRACTKnowledge about saturation and pressure distributions in a reservoir can help in determining an optimal drainage pattern, and in deciding on optimal well designs to reduce risks of blow‐outs and damage to production equipment. By analyzing time‐lapse PP AVO or time‐lapse multicomponent seismic data, it is possible to separate the effects of production related saturation and pressure changes on seismic data. To be able to utilize information about saturation and pressure distributions in reservoir model building and simulation, information about uncertainty in the estimates is useful. In this paper we present a method to estimate changes in saturation and pressure from time‐lapse multicomponent seismic data using a Bayesian estimation technique. Results of the estimations will be probability density functions (pdfs), giving immediate information about both parameter values and uncertainties. Linearized rock physical models are linked to the changes in saturation and pressure in the prior probability distribution. The relationship between the elastic parameters and the measured seismic data is described in the likelihood model. By assuming Gaussian distributed prior uncertainties the posterior distribution of the saturation and pressure changes can be calculated analytically. Results from tests on synthetic seismic data show that this method produces more precise estimates of changes in effective pressure than a similar methodology based on only PP AVO time‐lapse seismic data. This indicates that additional information about S‐waves obtained from converted‐wave seismic data is useful for obtaining reliable information about the pressure change distribution.
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A non‐linear regularized constrained impedance inversion
Authors Hongbing Zhang, Zuoping Shang and Changchun YangABSTRACTInversion for seismic impedance is an inherently complicated problem. It is ill‐posed and band‐limited. Thus the inversion results are non‐unique and the process is unstable. Combining regularization with constraints using sonic and density log data can help to reduce these problems. To achieve this, we developed an inversion method by constructing a new objective function, including edge‐preserving regularization and a soft constraint based on a Markov random field. The method includes the selection of proper initial values of the regularization parameters by a statistical method, and it adaptively adjusts the regularization parameters by the maximum likelihood method in a fast simulated‐annealing procedure to improve the inversion result and the convergence speed. Moreover, the method uses two kinds of regularization parameter: a ‘weighting factor’λ and a ‘scaling parameter’δ. We tested the method on both synthetic and field data examples. Tests on 2D synthetic data indicate that the inversion results, especially the aspects of the discontinuity, are significantly different for different regularization functions. The initial values of the regularization parameters are either too large or too small to avoid either an unstable or an over‐smoothed result, and they affect the convergence speed. When selecting the initial values of λ, the type of the regularization function should be considered. The results obtained by constant regularization parameters are smoother than those obtained by adaptively adjusting the regularization parameters. The inversion results of the field data provide more detailed information about the layers, and they match the impedance curves calculated from the well logs at the three wells, over most portions of the curves.
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Resolution analysis of geophysical images: Comparison between point spread function and region of data influence measures
Authors Carlyle R. Miller and Partha S. RouthABSTRACTPractical decisions are often made based on the subsurface images obtained by inverting geophysical data. Therefore it is important to understand the resolution of the image, which is a function of several factors, including the underlying geophysical experiment, noise in the data, prior information and the ability to model the physics appropriately. An important step towards interpreting the image is to quantify how much of the solution is required to satisfy the data observations and how much exists solely due to the prior information used to stabilize the solution. A procedure to identify the regions that are not constrained by the data would help when interpreting the image. For linear inverse problems this procedure is well established, but for non‐linear problems the procedure is more complicated. In this paper we compare two different approaches to resolution analysis of geophysical images: the region of data influence index and a resolution spread computed using point spread functions. The region of data influence method is a fully non‐linear approach, while the point spread function analysis is a linearized approach. An approximate relationship between the region of data influence and the resolution matrix is derived, which suggests that the region of data influence is connected with the rows of the resolution matrix. The point‐spread‐function spread measure is connected with the columns of the resolution matrix, and therefore the point‐spread‐function spread and the region of data influence are fundamentally different resolution measures. From a practical point of view, if two different approaches indicate similar interpretations on post‐inversion images, the confidence in the interpretation is enhanced. We demonstrate the use of the two approaches on a linear synthetic example and a non‐linear synthetic example, and apply them to a non‐linear electromagnetic field data example.
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Anisotropic reverse‐time migration for tilted TI media
Authors Xiang Du, John C. Bancroft and Larry R. LinesABSTRACTSeismic anisotropy in dipping shales results in imaging and positioning problems for underlying structures. We develop an anisotropic reverse‐time depth migration approach for P‐wave and SV‐wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. Based on an accurate phase velocity formula and dispersion relationships for weak anisotropy, we derive the wave equation for P‐wave and SV‐wave propagation in tilted transversely isotropic (TTI) media. The accuracy of the P‐wave equation and the SV‐wave equation is analyzed and compared with other acoustic wave equations for TTI media. Using this analysis and the pseudo‐spectral method, we apply reverse‐time migration to numerical and physical‐model data. According to the comparison between the isotropic and anisotropic migration results, the anisotropic reverse‐time depth migration offers significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.
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Equivalent time‐average and effective medium for periodic layers
Authors Alexey Stovas and Bjorn UrsinABSTRACTThe propagation of acoustic waves through a periodic layered medium is analyzed by an eigenvalue decomposition of the propagator matrix. This reveals how the velocity and attenuation of the layered medium vary as function of the periodic structure, material parameters and frequency. There are two important parameters which control the wave propagation in the periodic medium: the reflection coefficient and the ratio between one‐way traveltimes of the two parts of the cyclic layered medium.
For low frequencies (large values of wavelength to layer thickness), the layered structure behaves as an effective medium, then there is a transition zone, and for higher frequencies (small values of wavelength to layer thickness) the medium is described by the time‐average velocity.
In this paper we mostly concentrate on the transition zone between an effective medium and time‐average medium regimes. The width of the transition zone increases with larger values of the reflection coefficient. The transition zone corresponds to a blocking regime for which the transmission response of the layered structure is close to zero. For even higher frequencies, the time‐average medium is replaced by a new transition zone, and then again a time‐average medium. This pattern is periodically repeated with higher frequencies. For small values of the reflection coefficient, the transition between effective medium and time‐average medium occurs around a value of wavelength to layer thickness equal to 4.
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The iteration method for downward continuation of a potential field from a horizontal plane
Authors Shi‐zhe Xu, Jinyu Yang, Changfu Yang, Pengfei Xiao, Shengchang Chen and Zhihong GuoABSTRACTThis paper introduces an iteration method for the downward continuation of potential‐field data from a horizontal plane, and compares it with the conventional frequency‐domain method (Fourier transform) using 2D and 3D model tests. The paper evaluates the two methods in terms of the results, i.e. downward‐continuation distance and stability. The iteration method proves to be more stable and able to downward continue the potential for a greater distance than the Fourier transform method.
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Importance of borehole deviation surveys for monitoring of hydraulic fracturing treatments
Authors Petr Bulant, Leo Eisner, Ivan Pšenčík and Joël Le CalvezABSTRACTDuring seismic monitoring of hydraulic fracturing treatment, it is very common to ignore the deviations of the monitoring or treatment wells from their assumed positions. For example, a well is assumed to be perfectly vertical, but in fact, it deviates from verticality. This can lead to significant errors in the observed azimuth and other parameters of the monitored fracture‐system geometry derived from microseismic event locations. For common hydraulic fracturing geometries, a 2° deviation uncertainty on the positions of the monitoring or treatment well survey can cause a more than 20° uncertainty of the inverted fracture azimuths. Furthermore, if the positions of both the injection point and the receiver array are not known accurately and the velocity model is adjusted to locate perforations on the assumed positions, several‐millisecond discrepancies between measured and modeled SH‐P traveltime differences may appear along the receiver array. These traveltime discrepancies may then be misinterpreted as an effect of anisotropy, and the use of such anisotropic model may lead to the mislocation of the detected fracture system. The uncertainty of the relative positions between the monitoring and treatment wells can have a cumulative, nonlinear effect on inverted fracture parameters. We show that incorporation of borehole deviation surveys allows reasonably accurate positioning of the microseismic events. In this study, we concentrate on the effects of horizontal uncertainties of receiver and perforation positions. Understanding them is sufficient for treatment of vertical wells, and also necessary for horizontal wells.
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A real spectral analysis of the deformation of a homogenous electric field over a thin bed – A Hartley transform approach
Authors N. Sundararajan, Mansour A. Al‐Garni, G. Ramabrahmam and Y. SrinivasABSTRACTSpectral analysis of the deformation of a homogenous electric field caused by a long, thin inclined bed, which is of considerable importance in the exploration of ground water and minerals, is presented using the Hartley transform. The Hartley transform is an alternative and real replacement for the well‐known complex Fourier transform in the field of spectral analysis. The thickness of the bed and the inclination are given as functions of frequency by simple expressions. A theoretical example illustrates the method while the applicability is demonstrated by the field examples from the fractured crystalline basement complex in Burkina Faso, Africa and the Precambrian limestones of the Cuddapah basin, Andhra Pradesh, India. The results obtained by this method agree well with those of the drilling.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 63 (2015)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 55 (2007)
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Volume 52 (2004)
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Volume 40 (1992)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)